cv.complex variables – Sokhotski–Plemelj theorem (With Sqrt Term)

I am reading up on the Sokhotski-Plemelj theorem, and so far I’ve seen it being applied on equation with the general form (ref:

$$lim_{epsilonto0}frac{1}{x-x_0pm iepsilon} = Pfrac{1}{x-x_0} mp ipidelta(x-x_0)$$

Can the same theorem be applied to the following equation with an additional sqrt term?
$$lim_{epsilonto0}frac{1}{sqrt{x-x_0pm iepsilon}}$$

I can only think of bringing out the sqrt term and applying the formula to get the same result but with the additional sqrt term:

$$sqrt{lim_{epsilonto0}frac{1}{x-x_0pm iepsilon}} = sqrt{Pfrac{1}{x-x_0} mp ipidelta(x-x_0)}$$

Is there any way to simplify that? Or is there another way of applying the theorem? Thank you.